Missing data is a problem almost every behavioral researcher encounters. One promising technique, when data are missing, is to use maximum likelihood (ML) to directly estimate the model parameters and the sampling covariance matrix for the parameter estimates and use these estimated quantities to test hypotheses. These procedures are implemented in PROC Mixed in SAS and are therefore widely available. Although there have been some studies indicating the effectiveness of using ML, these studies have been conducted with sample sizes that are larger than those typically used in behavioral science. Thus, it is not clear how well these procedures perform with smaller sample sizes. For my dissertation, I plan to conduct a simulation study to estimate the Type I error and power of the Hotelling-Lawley-McKeon test statistic, based on ML estimates, in a repeated measures design with one between subjects factor. Specifically, I will investigate the effect of the following factors: sample size, the number of repeated and between subject levels, the covariance matrix for the repeated measures, percentage of data that are missing, and the missing data mechanism.